Static and dynamic properties of polymers in random media

The properties of polymers in a disordered environment are studied with emphasis on the effect of trapping due to fluctuations in the porosity of the environment. Results are obtained for $Z_N$, the number of self-avoiding walks of length N starting at the origin, and D, the diffusion coefficient for the center of mass of the polymer. The two most important new results are that 〈ln$Z_N$〉≊N-$a_1$ $N^{\alpha }$, with α=2-dν and ν the Flory exponent, and that the leading behavior of the diffusion coefficient is D≊exp(-$a_2$ $N^{\alpha }$).